Improved perturbation bounds for general quadratic matrix equations

Abstract

Perturbation analysis of general algebraic quadratic matrix equations is presented, which include as particular cases the standard and descriptor algebraic matrix Riccati equations, arising in the optimal control and filtering of continuous, time-invariant, linear systems. The perturbation bounds derived are superior to the bounds, already available in the literature. They are applicable to the error analysis of general quadratic matrix equations. The results are based on the use of Lyapunov majorants, fixed point principles and detailed estimates of the norms of tensor products of matrices.